When Albert borrows Willie's football there are 7 smaller boys running along with him. When their picture is being taken - and afterwards - there're only 6 smaller boys.
When Mrs. Barton is opening mail, she uses a letter opener then pulls the envelope flap out before removing a piece of paper. There is no point in using a letter opener if the flap is just tucked into the envelope.
Leslie's mom says that Albert must be related to Paul Bunyan. The earliest recorded reference to Paul Bunyan is from year 1904, and the earliest legends about him known are from late 1885. Overall, the Legend of Paul Bunyan was not born when this episode suppose to happened. However, according to Michael Edmonds in his book "Out of the Northwoods: The Many Lives of Paul Bunyan", stories about Bunyan were around for at least thirty years before they were published.
Albert pays the photographer 25 cents for the picture. In the 1800s a child could not afford to pay that kind of money for anything. Earlier in the series 5 cents was considered a lot of money for something. Though it would be difficult for a teenager to earn and save 25 cents, it was not impossible.
At 13:09 the photographer tells the boys to hold their breath for the picture. After the picture is taken, at 13:25 the little boy on the bottom left of the screen is still holding his breath long after the picture was taken.
When Albert becomes pen pals with Leslie, it is around 1880 to 1881. Leslie tells Albert in her letters that she is captain of the basketball team. This is impossible, since basketball was not invented until 1891, ten years after Albert and Leslie became pen pals.